Rotate pentagon QRSTU 90° counterclockwise to create pentagon Q’R’S’T’U’. Pentagon QRSTU is shown on the coordinate grid. Therefore, kite KLMN was rotated 180° about the origin to create kite K’L’M’N’. Let’s look at the rules, the only rule where the values of the x and y don’t switch but their sign changes is the 180° rotation. Let’s start by identifying the coordinates of the vertices of kite KLMN and of our rotated kite:Ī closer look at the coordinates of the vertices shows that the coordinates of K’L’M’N’ are the same as the vertices of the original kite but with the opposite sign. Can you identify which rotation of kite KLMN created kite K’L’M’N’? The kite has been rotated about the origin to create the kite K’L’M’N’. Kite KLMN is shown on the coordinate grid. Now I want you to try some practice problems on your own. Let’s apply the rules to the vertices to create quadrilateral A’B’C’D’: To rotate quadrilateral ABCD 90° counterclockwise about the origin we will use the rule \((x,y)\) becomes \((-y,x)\). Let’s apply the rule to the vertices to create the new triangle A’B’C’: Let’s rotate triangle ABC 180° about the origin counterclockwise, although, rotating a figure 180° clockwise and counterclockwise uses the same rule, which is \((x,y)\) becomes \((-x,-y)\), where the coordinates of the vertices of the rotated triangle are the coordinates of the original triangle with the opposite sign. To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x), where the y-value of the original point becomes the new \(x\)-value and the \(x\)-value of the original point becomes the new \(y\)-value with the opposite sign. Now that we know how to rotate a point, let’s look at rotating a figure on the coordinate grid. 270° counterclockwise rotation: \((x,y)\) becomes \((y,-x)\)Īs you can see, our two experiments follow these rules.180° clockwise and counterclockwise rotation: \((x,y)\) becomes \((-x,-y)\).Lucky for us, these experiments have allowed mathematicians to come up with rules for the most common rotations on a coordinate grid, assuming the origin, \((0,0)\), as the center of rotation. In our second experiment, point \(A (5,6)\) is rotated 180° counterclockwise about the origin to create \(A’ (-5,-6)\), where the \(x\)– and \(y\)-values are the same as point A but with opposite signs. In our first experiment, when we rotate point \(A (5,6)\) 90° clockwise about the origin to create point \(A’ (6,-5)\), the y-value of point A became the x-value of point A’ and the \(x\)-value of point A became the \(y\)-value of point A’ but with the opposite sign. Let’s take a closer look at the two rotations from our experiment. Here is the same point A at \((5,6)\) rotated 180° counterclockwise about the origin to get \(A’(-5,-6)\). Let’s look at a real example, here we plotted point A at \((5,6)\) then we rotated the paper 90° clockwise to create point A’, which is at \((6,-5)\). If you take a coordinate grid and plot a point, then rotate the paper 90° or 180° clockwise or counterclockwise about the origin, you can find the location of the rotated point. Let’s start by looking at rotating a point about the center \((0,0)\). Here is a figure rotated 90° clockwise and counterclockwise about a center point.Ī great math tool that we use to show rotations is the coordinate grid. We specify the degree measure and direction of a rotation. The angle of rotation is usually measured in degrees. The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. Another great example of rotation in real life is a Ferris Wheel where the center hub is the center of rotation. A figure can be rotated clockwise or counterclockwise. A figure and its rotation maintain the same shape and size but will be facing a different direction. We call this point the center of rotation. More formally speaking, a rotation is a form of transformation that turns a figure about a point. There are other forms of rotation that are less than a full 360° rotation, like a character or an object being rotated in a video game. The wheel on a car or a bicycle rotates about the center bolt. The earth is the most common example, rotating about an axis. Hello, and welcome to this video about rotation! In this video, we will explore the rotation of a figure about a point.
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Practice guideline update summary: mild cognitive impairment: report of the guideline development, dissemination, and implementation subcommittee of the American Academy of Neurology. Petersen RC, Lopez O, Armstrong MJ, et al. Brief cognitive tests for distinguishing clinical Alzheimer-type dementia from mild cognitive impairment or normal cognition in older adults with suspected cognitive impairment. Hemmy LS, Linskens EJ, Silverman PC, et al. 2020 Alzheimer's disease facts and figures. Rockville, Md.: Agency for Healthcare Research and Quality April 2020. (Prepared by the Minnesota Evidence-based Practice Center under contract no. Diagnosis and treatment of clinical Alzheimer's-type dementia: a systematic review. Jay Siwek, MD, Editor Emeritus Sumi Sexton, MD, Editor-in-Chiefįink HA, Hemmy LS, Linskens EJ, et al. 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The Mini-Mental State Examination (MMSE) had been freely available and widely disseminated after first being released in 1975. Wechsler Memory Scale logical memory Wechsler Adult Intelligence Scale digital symbol Boston Naming Test 60Įditor's Note: Dr. Trail Making Test part B, completion time Median prevalence of clinical Alzheimer-type dementia (range) |
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